Upper and lower bounds on the variances of linear combinations of the kth records. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Kozyra, Paweł Marcin; Rychlik, Tomasz
• Is Part Of: Statistics. Volume 52:Issue 1(2018)
• Page Start: 177
• Page End: 204
• Publication Date: 2018-01-02
• Subjects: kth record value -- linear combination -- kth record spacing -- variance -- sharp bound; 60E15 -- 62G32; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1343828
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We describe a method of determining upper bounds on the variances of linear combinations of the k th records values from i.i.d. sequences, expressed in terms of variances of parent distributions. We also present conditions for which the bounds are sharp, and those for which the respective lower ones are equal to zero. A special attention is paid to the case of the k th record spacings, i.e. the differences of consecutive k th record values.